Classical Mechanics (Kibble & Berkshire) · Problem 12.17

The calculus of variations and Hamilton's principle — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · lagrangian-mechanics-gravitational-central-force

Problem

A particle of mass

m

moves under the gravitational attraction of a fixed mass

M

situated at the origin. Take polar coordinates

r

\theta

as generalised coordinates and obtain Lagrange's equations. Show that

\theta

is a cyclic coordinate and find (and identify) the conserved momentum

p_\theta